Canard explosion in chemical and optical systems

Elena Shchepakina, Olga Korotkova

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

The paper deals with the study of the relation between the Andronov-Hopf bifurcation, the canard explosion and the critical phenomena for the van der Pol's type system of singularly perturbed differential equations. Suficient conditions for the limit cycle birth bifurcation in the case of the singularly perturbed systems are investigated. We use the method of integral manifolds and canards techniques to obtain the conditions under which the system possesses the canard cycle. Through the application to some chemical and optical models it is shown that the canard point should be considered as the critical value of the control parameter.

Original languageEnglish (US)
Pages (from-to)495-512
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume18
Issue number2
DOIs
StatePublished - Mar 2013

Fingerprint

Canard
Hopf bifurcation
Optical systems
Explosion
Optical System
Explosions
Differential equations
Integral Manifolds
Singularly Perturbed Systems
Critical Phenomena
Singularly Perturbed
Type Systems
Limit Cycle
Hopf Bifurcation
Control Parameter
Critical value
Bifurcation
Differential equation
Cycle

Keywords

  • Bifurcation
  • Canards
  • Chemical kinetics
  • Combustion
  • Optical systems
  • Semiconductor amplifier
  • Singular perturbations

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Canard explosion in chemical and optical systems. / Shchepakina, Elena; Korotkova, Olga.

In: Discrete and Continuous Dynamical Systems - Series B, Vol. 18, No. 2, 03.2013, p. 495-512.

Research output: Contribution to journalArticle

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